ON YAMABE-TYPE PROBLEMS ON RIEMANNIAN MANIFOLDS WITH BOUNDARY

Let (M, g) be an n-dimensional compact Riemannian manifold with boundary. We consider the Yamabe-type problem {-Delta(g)u + au = 0 on M, partial derivative(v)u + n-2/2bu = (n - 2)u(n / (n-2)+/-epsilon) on partial derivative M, where a is an element of C-1 (M), b is an element of C-1 (partial derivative M), v is the outward pointing unit normal to partial derivative M, Delta(g)u := div(g) del(g)u, and epsilon is a small positive parameter. We build solutions which blow up at a point of the boundary as epsilon goes to zero. The blowing-up behavior is ruled by the function b - H-g, where H-g is the boundary mean curvature.